Rust library for quantitative finance tools.

:dart: I want to hit a stable and legitimate v1.0.0 by the end of 2023, so any and all feedback, suggestions, or contributions are strongly welcomed!

Contact: rustquantcontact@gmail.com

Disclaimer: This is currently a free-time project and not a professional financial software library. Nothing in this library should be taken as financial advice, and I do not recommend you to use it for trading or making financial decisions.

:newspaper: Latest features

See CHANGELOG.md for a full list of changes.

Table of Contents

1. Automatic Differentiation - Reverse (Adjoint) Mode Automatic Differentiation.
2. Data - Methods for reading and writing data from/to various sources (CSV, JSON, PARQUET). Can also download data from Yahoo! Finance.
3. Distributions - PDFs, CDFs, MGFs, CFs, and other ditrubution related functions for common distributions.
4. Instruments - Various implementations for instruments like Bonds and Options, and the pricing of them. Others coming in the future (swaps, futures, CDSs, etc).
5. Mathematics - Numerical integration (double-exponential quadrature), root finding (gradient descent, Newton-Raphson), and risk-reward metrics.
6. Machine Learning - Currently only linear regression is implemented (and working on logistic regression). More to come in the future.
7. Money - Implementations for Cashflows, Currencies, and Quotes, and similar objects.
8. Stochastic Processes - Can generate Brownian Motion (standard, arithmetric and geometric) and various short-rate models (CIR, OU, Vasicek, Hull-White, etc).
9. Time and Dates - Time and date functionality. Mostly the DayCounter for pricing options and bonds.
10. Utilities/Helpers - Various helper functions and macros.
11. How-tos - How to do various things with RustQuant.
12. References - References and resources used for this project.

:link: Automatic Differentiation

Currently only gradients can be computed. Suggestions on how to extend the functionality to Hessian matrices are definitely welcome.

Additionally, only functions $f: \mathbb{R}^n \rightarrow \mathbb{R}$ (scalar output) are supported. However, you can manually apply the differentiation to multiple functions that could represent a vector output.

• Reverse (Adjoint) Mode
  • Implementation via Operator and Function Overloading.
  • Useful when number of outputs is smaller than number of inputs.
    • i.e for functions $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$, where $m \ll n$
• Forward (Tangent) Mode
  • Implementation via Dual Numbers.
  • Useful when number of outputs is larger than number of inputs.
    • i.e. for functions $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$, where $m \gg n$

use RustQuant::autodiff::*;

fn main() {
    // Create a new Graph to store the computations.
    let g = Graph::new();

    // Assign variables.
    let x = g.var(0.5);
    let y = g.var(4.2);

    // Define a function.
    let z = x * y + x.sin();

    // Accumulate the gradient.
    let grad = z.accumulate();

    println!("Function = {}", z);
    println!("Gradient = {:?}", grad.wrt([x, y]));
}

:bar_chart: Data

You can download data from Yahoo! Finance into a Polars DataFrame.

use RustQuant::data::*;
use time::macros::date;

fn main() {
    // New YahooFinanceData instance. 
    // By default, date range is: 1970-01-01 to present. 
    let mut yfd = YahooFinanceData::new("AAPL".to_string());

    // Can specify custom dates (optional). 
    yfd.set_start_date(time::macros::datetime!(2019 - 01 - 01 0:00 UTC));
    yfd.set_end_date(time::macros::datetime!(2020 - 01 - 01 0:00 UTC));

    // Download the historical data. 
    yfd.get_price_history();

    println!("Apple's quotes: {:?}", yfd.price_history)
}

Apple's quotes: Some(shape: (252, 7)
┌────────────┬───────────┬───────────┬───────────┬───────────┬────────────┬───────────┐
│ date       ┆ open      ┆ high      ┆ low       ┆ close     ┆ volume     ┆ adjusted  │
│ ---        ┆ ---       ┆ ---       ┆ ---       ┆ ---       ┆ ---        ┆ ---       │
│ date       ┆ f64       ┆ f64       ┆ f64       ┆ f64       ┆ f64        ┆ f64       │
╞════════════╪═══════════╪═══════════╪═══════════╪═══════════╪════════════╪═══════════╡
│ 2019-01-02 ┆ 38.7225   ┆ 39.712502 ┆ 38.557499 ┆ 39.48     ┆ 1.481588e8 ┆ 37.994499 │
│ 2019-01-03 ┆ 35.994999 ┆ 36.43     ┆ 35.5      ┆ 35.547501 ┆ 3.652488e8 ┆ 34.209969 │
│ 2019-01-04 ┆ 36.1325   ┆ 37.137501 ┆ 35.950001 ┆ 37.064999 ┆ 2.344284e8 ┆ 35.670372 │
│ 2019-01-07 ┆ 37.174999 ┆ 37.2075   ┆ 36.474998 ┆ 36.982498 ┆ 2.191112e8 ┆ 35.590965 │
│ …          ┆ …         ┆ …         ┆ …         ┆ …         ┆ …          ┆ …         │
│ 2019-12-26 ┆ 71.205002 ┆ 72.495003 ┆ 71.175003 ┆ 72.477501 ┆ 9.31212e7  ┆ 70.798401 │
│ 2019-12-27 ┆ 72.779999 ┆ 73.4925   ┆ 72.029999 ┆ 72.449997 ┆ 1.46266e8  ┆ 70.771545 │
│ 2019-12-30 ┆ 72.364998 ┆ 73.172501 ┆ 71.305    ┆ 72.879997 ┆ 1.441144e8 ┆ 71.191582 │
│ 2019-12-31 ┆ 72.482498 ┆ 73.419998 ┆ 72.379997 ┆ 73.412498 ┆ 1.008056e8 ┆ 71.711739 │
└────────────┴───────────┴───────────┴───────────┴───────────┴────────────┴───────────┘)

Read/write data

use RustQuant::data::*;

fn main() {
    // New `Data` instance.
    let mut data = Data::new(
        format: DataFormat::CSV, // Can also be JSON or PARQUET.
        path: String::from("./file/path/read.csv")
    )

    // Read from the given file. 
    data.read().unwrap();

    // New path to write the data to. 
    data.path = String::from("./file/path/write.csv")
    data.write().unwrap();

    println!("{:?}", data.data)
}

:bar_chart: Distributions

Probability density/mass functions, distribution functions, characteristic functions, etc.

• Gaussian
• Bernoulli
• Binomial
• Poisson
• Uniform (discrete & continuous)
• Chi-Squared
• Gamma
• Exponential

:chart_with_upwards_trend: Instruments

:chart_with_downwards_trend: Bonds

• Prices:
  • The Vasicek Model
  • The Cox, Ingersoll, and Ross Model
  • The Hull–White (One-Factor) Model
  • The Rendleman and Bartter Model
  • The Ho–Lee Model
  • The Black–Derman–Toy Model
  • The Black–Karasinski Model
• Duration
• Convexity

:money_with_wings: Option Pricing

• Closed-form price solutions:

  • Heston Model
  • Barrier
  • European
  • Greeks/Sensitivities
  • Lookback
  • Asian: Continuous Geometric Average
  • Forward Start
  • Basket
  • Rainbow
  • American

• Lattice models:

  • Binomial Tree (Cox-Ross-Rubinstein)

The stochastic process generators can be used to price path-dependent options via Monte-Carlo.

• Monte Carlo pricing:
  • Lookback
  • Asian
  • Chooser
  • Barrier

use RustQuant::options::*;

fn main() {
    let VanillaOption = EuropeanOption {
        initial_price: 100.0,
        strike_price: 110.0,
        risk_free_rate: 0.05,
        volatility: 0.2,
        dividend_rate: 0.02,
        time_to_maturity: 0.5,
    };

    let prices = VanillaOption.price();

    println!("Call price = {}", prices.0);
    println!("Put price = {}", prices.1);
}

:triangular_ruler: Mathematics

Optimization and Root Finding

• Gradient Descent
• Newton-Raphson

Note: the reason you need to specify the lifetimes and use the type Variable is because the gradient descent optimiser uses the RustQuant::autodiff module to compute the gradients. This is a slight inconvenience, but the speed-up is enormous when working with functions with many inputs (when compared with using finite-difference quotients).

use RustQuant::optimisation::GradientDescent;

// Define the objective function.
fn himmelblau<'v>(variables: &[Variable<'v>]) -> Variable<'v> {
    let x = variables[0];
    let y = variables[1];

    ((x.powf(2.0) + y - 11.0).powf(2.0) + (x + y.powf(2.0) - 7.0).powf(2.0))
}

fn main() {
    // Create a new GradientDescent object with:
    //      - Step size: 0.005 
    //      - Iterations: 10000
    //      - Tolerance: sqrt(machine epsilon)
    let gd = GradientDescent::new(0.005, 10000, std::f64::EPSILON.sqrt() );

    // Perform the optimisation with:
    //      - Initial guess (10.0, 10.0),
    //      - Verbose output.
    let result = gd.optimize(&himmelblau, &vec![10.0, 10.0], true);
    
    // Print the result.
    println!("{:?}", result.minimizer);
}

Integration

• Numerical Integration (needed for Heston model, for example):
  • Tanh-Sinh (double exponential) quadrature
  • Composite Midpoint Rule
  • Composite Trapezoidal Rule
  • Composite Simpson's 3/8 Rule

use RustQuant::math::*;

fn main() {
    // Define a function to integrate: e^(sin(x))
    fn f(x: f64) -> f64 {
        (x.sin()).exp()
    }

    // Integrate from 0 to 5.
    let integral = integrate(f, 0.0, 5.0);

    // ~ 7.18911925
    println!("Integral = {}", integral); 
}

Risk-Reward Metrics

• Risk-Reward Measures (Sharpe, Treynor, Sortino, etc)

:crystal_ball: Machine Learning

Regression

• Linear (using QR or SVD decomposition)
• Logistic (using MLE or IRLS). Work in progress.

:moneybag: Money

• Cashflows
• Currencies
• Quotes

:chart_with_upwards_trend: Stochastic Processes and Short Rate Models

The following is a list of stochastic processes that can be generated.

• Brownian Motion
• Arithmetic Brownian Motion
  • $dX(t) = \mu dt + \sigma dW(t)$
• Geometric Brownian Motion
  • $dX(t) = \mu X(t) dt + \sigma X(t) dW(t)$
  • Models: Black-Scholes (1973), Rendleman-Bartter (1980)
• Cox-Ingersoll-Ross (1985)
  • $dX(t) = \left[ \theta - \alpha X(t) \right] dt + \sigma \sqrt{r_t} dW(t)$
• Ornstein-Uhlenbeck process
  • $dX(t) = \theta \left[ \mu - X(t) \right] dt + \sigma dW(t)$
  • Models: Vasicek (1977)
• Ho-Lee (1986)
  • $dX(t) = \theta(t) dt + \sigma dW(t)$
• Hull-White (1990)
  • $dX(t) = \left[ \theta(t) - \alpha X(t) \right]dt + \sigma dW(t)$
• Extended Vasicek (1990)
  • $dX(t) = \left[ \theta(t) - \alpha(t) X(t) \right] dt + \sigma dW(t)$
• Black-Derman-Toy (1990)
  • $d\ln[X(t)] = \left[ \theta(t) + \frac{\sigma'(t)}{\sigma(t)}\ln[X(t)] \right]dt + \sigma_t dW(t)$
  • $d\ln[X(t)] = \theta(t) dt + \sigma dW(t)$

use RustQuant::stochastics::*;

fn main() {
    // Create new GBM with mu and sigma.
    let gbm = GeometricBrownianMotion::new(0.05, 0.9);

    // Generate path using Euler-Maruyama scheme.
    // Parameters: x_0, t_0, t_n, n, sims, parallel.
    let output = (&gbm).euler_maruyama(10.0, 0.0, 0.5, 10, 1, false);

    println!("GBM = {:?}", output.paths);
}

:handshake: Helper Functions and Macros

A collection of utility functions and macros.

• Plot a vector.
• Write vector to file.
• Cumulative sum of vector.
• Linearly spaced sequence.
• assert_approx_equal!

:heavy_check_mark: How-tos

See /examples for more details. Run them with:

cargo run --example automatic_differentiation

I would not recommend using RustQuant within any other libraries for some time, as it will most likely go through many breaking changes as I learn more Rust and settle on a decent structure for the library.

:pray: I would greatly appreciate contributions so it can get to the v1.0.0 mark ASAP.

:book: References:

• John C. Hull - Options, Futures, and Other Derivatives
• Damiano Brigo & Fabio Mercurio - Interest Rate Models - Theory and Practice (With Smile, Inflation and Credit)
• Paul Glasserman - Monte Carlo Methods in Financial Engineering
• Andreas Griewank & Andrea Walther - Evaluating Derivatives - Principles and Techniques of Algorithmic Differentiation
• Steven E. Shreve - Stochastic Calculus for Finance II: Continuous-Time Models
• Espen Gaarder Haug - Option Pricing Formulas
• Antoine Savine - Modern Computational Finance: AAD and Parallel Simulations